2198:
disguised as solitons. This raises an important conceptual point. The magnetic monopole here has been treated as bona fide particle even though it arose as a soliton, namely as a solution to the classical equations of motion. It therefore appears to have a different status from the “Planckian particles” considered hitherto and discussed at the beginning of the lecture. These arose as quantum excitations of the original fields of the initial formulation of the theory, products of the quantisation procedures applied to these dynamical variables (fields).
31:
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states that if we understand the "fundamental" or "elementary" parts of a system we can then deduce all the properties of the system as a whole. Duality says that there is no physically measurable property that can deduce what is fundamental and what is not, the notion of what is elementary and what
2197:
The first conclusion is that Dirac’s explanation of charge quantisation is triumphantly vindicated. At first sight it seemed as if the idea of unification provided an alternative explanation, avoiding monopoles, but this was illusory as magnetic monopoles were indeed lurking hidden in the theory,
1632:
conjectured that at strong coupling the situation would be reversed: the electrically charged objects would be strongly coupled and have non-singular cores, while the magnetically charged objects would become weakly coupled and point like. The strongly coupled theory would be equivalent to weakly
2182:
I could go on and on, taking you on a tour of the space of string theories, and show you how everything is mutable, nothing being more elementary than anything else. Personally, I would bet that this kind of anti-reductionist behaviour is true in any consistent synthesis of quantum mechanics and
1471:
The interest of the theory of magnetic poles is that it forms a natural generalization of the usual electrodynamics and it leads to the quantization of electricity. The quantization of electricity is one of the most fundamental and striking features of atomic physics, and there seems to be no
2167:
Under a duality map, often an elementary particle in one string theory gets mapped to a composite particle in a dual string theory and vice versa. Thus classification of particles into elementary and composite loses significance as it depends on which particular theory we use to describe the
1667:
supersymmetric version (N is the number of conserved supersymmetries), there were no quantum corrections to the classical mass spectrum and the calculation of the exact masses could be obtained. The problem related to the monopole's unit spin remained for this
1122:{\displaystyle {\begin{aligned}\nabla \cdot \mathbf {E} &=\rho \quad &\nabla \times \mathbf {E} +{\dot {\mathbf {B} }}&=0\\\nabla \cdot \mathbf {B} &=0\quad &\nabla \times \mathbf {B} -{\dot {\mathbf {E} }}&=\mathbf {j} .\end{aligned}}}
1467:. This would "explain" why the magnitude of the electron charge and proton charge should be exactly equal and are the same no matter what electron or proton we are considering, a fact known to hold true to one part in 10. This led Dirac to state:
1408:
1720:
supersymmetry: Hugh Osborn was able to show that when spontaneous symmetry breaking is imposed in the N = 4 supersymmetric gauge theory, the spins of the topological monopole states are identical to those of the massive gauge particles.
2252:
The term S-duality began being used in the first proposals for extending the strong/weak duality conjecture from the case of supersymmetric four dimensional Yang–Mills theories to the context of superstring theory, first used by
1997:
1620:
2103:
1237:
1204:
1341:
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was studying the quantum mechanics of an electric charge moving in a magnetic monopole field, and he found he could only consistently define the wavefunction if the electric charge
2035:
1792:
1465:
1284:
1262:
1174:
1152:
2154:
The
Montonen–Olive duality throws into question the idea that we can obtain a full theory of physics by reducing things into their "fundamental" parts. The philosophy of
1543:, the electrically and magnetically charged objects look very different: one an electron point particle that is weakly coupled and the other a monopole soliton that is
1336:
2211:
However, this argument bears little consequence to the reality of string theory as a whole, and perhaps a better perspective might quest for the implications of the
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2163:, as both the Noether charge (particle) and topological charge (soliton) have the same ontology. Several notable physicists underlined the implications of duality:
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1819:
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There should be two "dual equivalent" field formulations of the same theory in which electric (Noether) and magnetic (topological) quantum numbers exchange roles.
2146:
is an integer depending on the choice of gauge group. In the case the theta-angle is 0, this reduces to the simple form of
Montonen–Olive duality stated above.
1431:
1328:
1308:
2309:
is a more general analysis of the relativistic classical and quantum dynamics of a system of moving and interacting magnetic monopoles and electric charges.
3489:
2732:
Bekaert, Xavier; Boulanger, Nicolas; Henneaux, Marc (2003-02-26). "Consistent deformations of dual formulations of linearized gravity: A no-go result".
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1933:
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coupled theory in which the basic quanta carried magnetic rather than electric charges. In subsequent work this conjecture was refined by
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the name is a "historical accident": it was introduced, for reasons of practicality, to indicate the discrete symmetry group SL(2,
4531:
1886:, which is the case where the Montonen–Olive duality applies, one obtains a physically equivalent theory if one replaces the gauge
1550:
866:; the viewpoints are equivalent and the situation dependent on the duality. It was later proven to hold true when dealing with a
803:
4572:
4246:
2265:) of the ten-dimensional heterotic string theory compactified to four dimensions. More details can be found, for example, in
1472:
explanation for it apart from the theory of poles. This provides some grounds for believing in the existence of these poles.
4582:
2058:
1209:
1179:
1176:
in these equations is striking. If one ignores the sources, or adds magnetic sources, the equations are invariant under
4860:
4271:
2628:
Freund, Peter G. O.; Nambu, Yoichiro (1968-10-25). "Scalar Fields
Coupled to the Trace of the Energy-Momentum Tensor".
1529:
913:
177:
3916:(1994). "Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory".
5232:
4698:
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182:
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937:
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Godazgar, Hadi; Godazgar, Mahdi; Nicolai, Hermann (February 2014). "Generalised geometry from the ground up".
1544:
1540:
5404:
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4853:
4264:
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Ogievetsky, V.I; Polubarinov, I.V (November 1965). "Interacting field of spin 2 and the einstein equations".
1500:
5849:
5174:
4905:
3701:
2008:
1490:
574:
4139:
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Osborn, H. (1979). "Topological charges for N = 4 supersymmetric gauge theories and monopoles of spin 1".
4605:
4521:
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4445:
4306:
796:
5429:
3816:
Studies in
History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
3080:
Studies in
History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
5350:
5002:
1867:
of
Ogievetsky–Polubarinov theory. The dual field is coupled to the curl of the energy momentum tensor.
2159:
is composite is merely relative, acting as a kind of gauge symmetry. This seems to favour the view of
1763:
1532:, previously magnetic monopoles had always included a point singularity. The subject was motivated by
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Philosophical
Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
1403:{\displaystyle {\begin{aligned}eq=2\pi \hbar n\quad \quad &n=0,\pm 1,\pm 2...\\\end{aligned}}}
1267:
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Alshal, H.; Curtright, T. L. (September 2019). "Massive dual gravity in N spacetime dimensions".
2220:
953:
739:
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251:
161:
93:
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treated the case of an electrically charged particle moving in a fixed magnetic monopole field.
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965:
932:, being viewed as amongst the most important. These dualities have played an important role in
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The idea of a close similarity between electricity and magnetism, going back to the time of
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The massless linearized dual gravity was theoretically realized in 2000s for wide class of
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324:
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81:
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1729:
In 1979–1980, Montonen–Olive duality motivated developing mixed symmetric higher-spin
5939:
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5679:
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3229:
3183:
3143:
3103:
3048:
3013:
3001:
2889:
2840:
2828:
2767:
2706:
2671:
Hull, Christopher M (2001-09-24). "Duality in gravity and higher spin gauge fields".
2653:
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4001:
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3274:
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3120:
Proceedings of the Royal
Society A: Mathematical, Physical and Engineering Sciences
3095:
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2759:
2718:
2698:
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2608:
2559:
2524:
2453:
2436:
Nielsen, H.B.; Olesen, P. (September 1973). "Vortex-line models for dual strings".
1738:
1547:. The magnetic fine structure constant is roughly the reciprocal of the usual one:
674:
609:
579:
459:
399:
364:
309:
299:
156:
45:
5554:
3974:(1995). "Electric-magnetic duality in supersymmetric non-Abelian gauge theories".
3744:(2016). "Maxwell electromagnetism as an emergent phenomenon in condensed matter".
831:
according to current terminology. It generalizes the electro-magnetic symmetry of
279:
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5984:
5934:
5919:
5909:
5804:
5769:
5594:
5164:
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4749:
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4236:
1927:
The gauge coupling and theta-angle can be combined to form one complex coupling
1902:
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1730:
957:
759:
714:
659:
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634:
529:
494:
319:
223:
5874:
4814:
3835:
3099:
2997:
2885:
2824:
2793:
West, Peter (February 2012). "Generalised geometry, eleven dimensions and E11".
2542:
Curtright, Thomas L.; Freund, Peter G.O. (January 1980). "Massive dual fields".
599:
6004:
5999:
5959:
5899:
5729:
5719:
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5709:
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5619:
5614:
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5169:
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4789:
4435:
4420:
3971:
3909:
3677:
3481:
3465:
3427:
2763:
2290:
1876:
1750:
1733:. For the spin-2 case, the gauge-transformation dynamics of Curtright field is
1625:
882:
878:
843:
734:
729:
689:
624:
454:
444:
439:
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349:
344:
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289:
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5809:
4111:
1897:. This also involves an interchange of the electrically charged particles and
614:
534:
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4013:
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3524:
3385:
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3237:
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3147:
3107:
3005:
2893:
2832:
2771:
2710:
2657:
2649:
2049:
1909:
1734:
1493:
independently constructed monopoles not as quantized point particles, but as
917:
724:
709:
684:
669:
639:
584:
559:
489:
484:
449:
424:
414:
384:
228:
50:
22:
5779:
3255:"Strong-weak coupling duality and non-perturbative effects in string theory"
504:
6024:
5864:
5744:
5694:
5664:
5649:
5457:
5424:
5316:
5242:
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2155:
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1742:
754:
589:
469:
419:
389:
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233:
6019:
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5704:
5654:
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5388:
5149:
5106:
4824:
4799:
4794:
4744:
4723:
4688:
4683:
4410:
4186:
3576:
3485:
3434:(2006). "Electric-Magnetic Duality And The Geometric Langlands Program".
3349:
3298:
2160:
1921:
1629:
1433:
exists anywhere, then all electric charges must be multiples of the unit
886:
749:
719:
699:
554:
509:
464:
429:
379:
4046:
1485:
The magnetic monopole line of research took a step forward in 1974 when
5964:
5904:
5839:
5502:
5482:
5381:
5340:
5154:
4728:
4718:
4703:
4495:
4415:
4379:
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3988:
3930:
3868:
3660:
3589:
3448:
3410:
3212:
3155:
3115:
2746:
2685:
1992:{\displaystyle \tau ={\frac {\theta }{2\pi }}+{\frac {4\pi i}{g^{2}}}.}
1637:
and David Olive, they showed that in a supersymmetric extension of the
1287:
694:
629:
564:
256:
30:
5879:
5669:
5609:
5255:
5129:
5050:
5045:
5040:
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4678:
4567:
4182:
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3913:
3431:
1634:
859:
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828:
604:
394:
334:
120:
115:
110:
16:
Strong-weak duality in supersymmetric theories of theoretical physics
3353:
3254:
2227:
is at its strongest a self-justification for any unprovable theory.
5525:
5414:
5409:
5139:
5134:
5071:
4987:
4713:
4708:
4693:
4668:
4189:(1978). "Supersymmetry algebras that include topological charges".
3758:
2980:
2933:
2595:
2219:. Since experimentally tested evidence bears no resemblance to the
1753:
field, that is coupled to the trace of its energy–momentum tensor.
1694:
case, but soon after a solution to it was obtained for the case of
130:
125:
2868:
2807:
5144:
5124:
5081:
5076:
4673:
1494:
874:
60:
4845:
4256:
3118:(1931). "Quantised Singularities in the Electromagnetic Field".
4450:
4440:
2507:
Curtright, Thomas (December 1985). "Generalized gauge fields".
1737:
in D>4 spacetime. Meanwhile, the spin-0 field, developed by
3809:"Dual theories: 'Same but different' or 'different but same'?"
5116:
4663:
3581:
Lecture at the
Symposium "One Hundred Years of H", Pavia 2000
1413:
Note that from the above if just one monopole of some charge
55:
2044:(but not the classical theory, except in the case when the
1615:{\displaystyle \alpha _{m}q^{2}/4\pi \hbar =n^{2}/4\alpha }
924:. This duality is now one of several in string theory, the
3854:(1997). "Lectures on superstring and M theory dualities".
3396:(1996). "Magnetic Monopoles, Duality, and Supersymmetry".
2395:
2393:
2464:
2344:
2342:
3198:; Khuri, Ramzi R.; Lu, J. X. (1995). "String solitons".
2731:
2405:
2002:
Since the theta-angle is periodic, there is a symmetry
2853:
2476:
2390:
3253:
Font, A.; Ibáñez, L.E.; Lüst, D.; Quevedo, F. (1990).
2339:
968:
for a unified theory of electric and magnetic fields:
4032:(2001). "Recent developments in superstring theory".
3026:
2125:
2098:{\displaystyle \tau \mapsto {\frac {-1}{n_{G}\tau }}}
2061:
2011:
1936:
1827:
1800:
1766:
1700:
1674:
1647:
1553:
1503:
1439:
1419:
1339:
1316:
1296:
1270:
1248:
1232:{\displaystyle \mathbf {B} \rightarrow -\mathbf {E} }
1212:
1182:
1160:
1138:
977:
889:
after they proposed the idea in their academic paper
2417:
2282:, like the Montonen–Olive duality, is also valid in
1199:{\displaystyle \mathbf {E} \rightarrow \mathbf {B} }
920:, especially since the 1990s with the advent of the
2366:
2354:
1851:A massive spin-2 dual gravity, to lowest order, in
4241:. Cambridge, England: Cambridge University Press.
2488:
2138:
2097:
2029:
1991:
1840:
1813:
1786:
1712:
1686:
1659:
1614:
1521:
1459:
1425:
1402:
1322:
1302:
1278:
1256:
1231:
1198:
1168:
1146:
1121:
6042:
2378:
2243:Or weak–strong duality, both terms are correct.
3706:"Particle Spectrum in the Quantum Field Theory"
2965:
2914:
2541:
2040:The quantum mechanical theory with gauge group
1863:is recently introduced as a theory dual to the
4140:"Magnetic monopoles in unified gauge theories"
3908:
3426:
3293:
4861:
4272:
3531:
3480:
2915:Curtright, T.L.; Alshal, H. (November 2019).
2470:
2435:
2149:
904:
891:
797:
4134:
3739:
3354:"Magnetic monopoles in gauge field theories"
3344:
2411:
2215:, and such deep mathematical connections as
947:
4181:
4034:Nuclear Physics B - Proceedings Supplements
3856:Nuclear Physics B - Proceedings Supplements
3436:Communications in Number Theory and Physics
3252:
3194:
2627:
2482:
2254:
4868:
4854:
4279:
4265:
3642:
3070:
2399:
2348:
2323:
1242:Why should there be such symmetry between
804:
790:
29:
4234:
4045:
3987:
3929:
3867:
3757:
3659:
3588:
3447:
3409:
3211:
2979:
2950:
2932:
2867:
2806:
2745:
2684:
2612:
2594:
2576:
2506:
1870:
854:), can in fact be viewed as "elementary"
4086:
3700:
3490:"Magnetic monopoles as gauge particles?"
3158:(1948). "The Theory of Magnetic Poles".
2579:"Massive dual spinless fields revisited"
2423:
2188:
862:playing the reverse role of "composite"
3970:
3850:
3806:
3579:(2001). "The Quantisation of Charges".
2360:
2319:
2266:
2052:) is also invariant under the symmetry
912:S-duality is now a basic ingredient in
6043:
4235:Olive, D.; West, P. C. (8 July 1999).
3605:
3392:
2577:Curtright, Thomas L. (November 2019).
2494:
2372:
1522:{\displaystyle \operatorname {SU} (2)}
892:Magnetic monopoles as gauge particles?
4849:
4260:
3575:
3537:"Vortex-line models for dual strings"
3154:
3114:
2384:
2306:
2302:
2203:
2030:{\displaystyle \tau \mapsto \tau +1.}
1477:
5266:Bogomol'nyi–Prasad–Sommerfield bound
3303:"Gauge theories and magnetic charge"
2792:
2670:
2287:= 4 supersymmetric Yang–Mills theory
1330:satisfy the quantization condition:
871:= 4 supersymmetric Yang–Mills theory
846:that are "composite" (i.e. they are
247:= 4 supersymmetric Yang–Mills theory
4238:Duality and Supersymmetric Theories
4028:
2173:
960:, was first made more precise with
13:
3073:"Duality and 'particle' democracy"
3058:
2112:is simultaneously replaced by its
1771:
1768:
1072:
1048:
1006:
982:
938:fractional charges of the electron
914:topological quantum field theories
178:Geometric Langlands correspondence
14:
6067:
4875:
4286:
3398:High Energy Physics and Cosmology
1585:
1446:
1359:
4312:Supersymmetric quantum mechanics
1787:{\displaystyle \mathrm {SO} (8)}
1760:, especially that is related to
1272:
1250:
1225:
1214:
1192:
1184:
1162:
1140:
1108:
1090:
1079:
1055:
1024:
1013:
989:
5463:Eleven-dimensional supergravity
3020:
2959:
2952:10.1016/j.nuclphysb.2019.114777
2917:"Massive dual spin 2 revisited"
2908:
2847:
2786:
2725:
2664:
2621:
2614:10.1016/j.nuclphysb.2019.114784
2570:
2535:
2500:
2429:
2312:
1924:are transformed non-trivially.
1908:In fact, there exists a larger
1724:
1366:
1365:
1069:
1003:
823:is the oldest known example of
3358:Reports on Progress in Physics
2968:Journal of High Energy Physics
2856:Journal of High Energy Physics
2795:Journal of High Energy Physics
2673:Journal of High Energy Physics
2296:
2272:
2246:
2237:
2065:
2015:
1781:
1775:
1516:
1510:
1218:
1188:
839:, which are usually viewed as
1:
4911:Second superstring revolution
4064:10.1016/S0920-5632(01)00929-X
3886:10.1016/S0920-5632(97)00070-4
2703:10.1088/1126-6708/2001/09/027
2333:
1460:{\displaystyle 2\pi \hbar /q}
922:second superstring revolution
5405:Generalized complex manifold
4906:First superstring revolution
4211:10.1016/0370-2693(78)90357-X
4167:10.1016/0550-3213(74)90486-6
4006:10.1016/0550-3213(94)00023-8
3948:10.1016/0550-3213(94)90124-4
3628:10.1016/0370-2693(79)91118-3
3561:10.1016/0550-3213(73)90350-7
3517:10.1016/0370-2693(77)90076-4
3330:10.1016/0550-3213(77)90221-8
3279:10.1016/0370-2693(90)90523-9
3230:10.1016/0370-1573(95)00002-X
3049:10.1016/0003-4916(65)90077-1
2564:10.1016/0550-3213(80)90174-1
2529:10.1016/0370-2693(85)91235-3
2458:10.1016/0550-3213(73)90350-7
2289:and was proposed in 1997 by
1491:Alexander Markovich Polyakov
1279:{\displaystyle \mathbf {B} }
1257:{\displaystyle \mathbf {E} }
1169:{\displaystyle \mathbf {B} }
1147:{\displaystyle \mathbf {E} }
7:
4307:Supersymmetric gauge theory
3836:10.1016/j.shpsb.2015.09.005
3100:10.1016/j.shpsb.2016.03.002
2223:; where philosophically an
905:Montonen & Olive (1977)
10:
6072:
5003:Non-critical string theory
4606:Pure 4D N = 1 supergravity
3678:10.1103/RevModPhys.68.1245
3646:(1996). "String duality".
3466:10.4310/CNTP.2007.v1.n1.a1
3378:10.1088/0034-4885/41/9/001
2764:10.1103/PhysRevD.67.044010
2150:Philosophical implications
940:, to the discovery of the
5547:
5524:
5501:
5448:
5333:
5241:
5183:
5115:
5064:
5031:
4926:
4883:
4737:
4654:
4596:
4540:
4514:
4506:Electric–magnetic duality
4403:
4340:
4294:
4112:10.1007/s10701-011-9620-x
4090:(2011). "String Theory".
3648:Reviews of Modern Physics
2471:Montonen & Olive 1977
948:Electric–magnetic duality
821:electric–magnetic duality
5539:Introduction to M-theory
5233:Wess–Zumino–Witten model
5175:Hanany–Witten transition
4901:History of string theory
4527:Haag–Łopuszański–Sohnius
4501:Little hierarchy problem
2650:10.1103/PhysRev.174.1741
2230:
1758:higher-spin gauge fields
934:condensed matter physics
928:which gives rise to the
103:Non-perturbative results
5218:Vertex operator algebra
4918:String theory landscape
4583:6D (2,0) superconformal
3071:Castellani, E. (2016).
2998:10.1007/JHEP09(2019)063
2886:10.1007/JHEP02(2014)075
2825:10.1007/JHEP02(2012)018
2483:Witten & Olive 1978
2221:String theory landscape
1534:Nielsen–Olesen vortices
1530:Yang–Mills–Higgs system
5516:AdS/CFT correspondence
5271:Exceptional Lie groups
5213:Superconformal algebra
5185:Conformal field theory
5056:Montonen–Olive duality
5008:Non-linear sigma model
4563:N = 4 super Yang–Mills
4553:N = 1 super Yang–Mills
4461:Supersymmetry breaking
4365:Superconformal algebra
4360:Super-Poincaré algebra
4092:Foundations of Physics
3776:10.1098/rsta.2016.0093
3180:10.1103/PhysRev.74.817
3140:10.1098/rspa.1931.0130
2280:AdS/CFT correspondence
2213:AdS/CFT correspondence
2209:
2194:
2179:
2140:
2108:while the gauge group
2099:
2031:
1993:
1875:In a four-dimensional
1871:Mathematical formalism
1842:
1841:{\displaystyle E_{11}}
1815:
1788:
1714:
1688:
1661:
1616:
1523:
1483:
1461:
1427:
1404:
1324:
1304:
1280:
1258:
1233:
1200:
1170:
1148:
1123:
964:'s formulation of his
926:AdS/CFT correspondence
910:
817:Montonen–Olive duality
219:Conformal field theory
136:AdS/CFT correspondence
5511:Holographic principle
5478:Type IIB supergravity
5473:Type IIA supergravity
5325:-form electrodynamics
4944:Bosonic string theory
4641:Type IIB supergravity
4636:Type IIA supergravity
4611:4D N = 1 supergravity
4476:Seiberg–Witten theory
4390:Super Minkowski space
4370:Supersymmetry algebra
3535:; Olesen, P. (1973).
2195:
2180:
2165:
2141:
2139:{\displaystyle n_{G}}
2100:
2032:
1994:
1843:
1816:
1814:{\displaystyle E_{7}}
1789:
1715:
1689:
1662:
1617:
1524:
1469:
1462:
1428:
1405:
1325:
1305:
1281:
1259:
1234:
1201:
1171:
1149:
1132:The symmetry between
1124:
930:holographic principle
897:
262:Holographic principle
239:Twistor string theory
5430:Hořava–Witten theory
5377:Hyperkähler manifold
5065:Particles and fields
5013:Tachyon condensation
4998:Matrix string theory
4426:Short supermultiplet
3807:Rickles, D. (2015).
2123:
2114:Langlands dual group
2059:
2009:
1934:
1916:symmetry where both
1825:
1798:
1764:
1698:
1672:
1645:
1639:Georgi–Glashow model
1551:
1501:
1437:
1417:
1337:
1314:
1310:and magnetic charge
1294:
1268:
1246:
1210:
1180:
1158:
1136:
975:
873:. It is named after
864:topological solitons
214:Theory of everything
5468:Type I supergravity
5372:Calabi–Yau manifold
5367:Ricci-flat manifold
5346:Kaluza–Klein theory
5087:Ramond–Ramond field
4993:String field theory
4646:Gauged supergravity
4631:Type I supergravity
4588:ABJM superconformal
4385:Harmonic superspace
4203:1978PhLB...78...97W
4159:1974NuPhB..79..276T
4104:2013FoPh...43..174S
4056:2001NuPhS..94...35S
3998:1995NuPhB.435..129S
3940:1994NuPhB.426...19S
3878:1997NuPhS..55....1S
3828:2017SHPMP..59...62R
3768:2016RSPTA.37460093R
3725:1974JETPL..20..194P
3670:1996RvMP...68.1245P
3620:1979PhLB...83..321O
3599:2001hep.th....4063O
3553:1973NuPhB..61...45N
3509:1977PhLB...72..117M
3458:2007CNTP....1....1K
3420:1997hepcbconf...66H
3370:1978RPPh...41.1357G
3322:1977NuPhB.125....1G
3271:1990PhLB..249...35F
3222:1995PhR...259..213D
3172:1948PhRv...74..817D
3132:1931RSPSA.133...60D
3092:2017SHPMP..59..100C
3041:1965AnPhy..35..167O
2990:2019JHEP...09..063A
2943:2019NuPhB.94814777C
2878:2014JHEP...02..075G
2817:2012JHEP...02..018W
2756:2003PhRvD..67d4010B
2695:2001JHEP...09..027H
2642:1968PhRv..174.1741F
2605:2019NuPhB.94814784C
2556:1980NuPhB.172..413C
2521:1985PhLB..165..304C
2450:1973NuPhB..61...45N
2225:Anthropic principle
2217:Monstrous moonshine
1713:{\displaystyle N=4}
1687:{\displaystyle N=2}
1660:{\displaystyle N=2}
962:James Clerk Maxwell
856:quantized particles
852:topological defects
833:Maxwell's equations
825:strong–weak duality
252:Kaluza–Klein theory
188:Monstrous moonshine
69:Perturbative theory
38:Fundamental objects
5435:K-theory (physics)
5312:ADE classification
4949:Superstring theory
4621:Higher dimensional
4616:N = 8 supergravity
4532:Nonrenormalization
4327:Super vector space
4322:Superstring theory
3752:(2075): 20160093.
2255:Font et al. (1990)
2136:
2095:
2027:
1989:
1899:magnetic monopoles
1838:
1811:
1784:
1710:
1684:
1657:
1612:
1519:
1457:
1423:
1400:
1398:
1320:
1300:
1276:
1254:
1229:
1196:
1166:
1144:
1119:
1117:
954:André-Marie Ampère
936:, from predicting
895:where they state:
837:magnetic monopoles
6038:
6037:
5820:van Nieuwenhuizen
5356:Why 10 dimensions
5261:Chern–Simons form
5228:Kac–Moody algebra
5208:Conformal algebra
5203:Conformal anomaly
5097:Magnetic monopole
5092:Kalb–Ramond field
4934:Nambu–Goto action
4843:
4842:
4486:Wess–Zumino gauge
4248:978-0-521-64158-6
4191:Physics Letters B
4147:Nuclear Physics B
3976:Nuclear Physics B
3918:Nuclear Physics B
3608:Physics Letters B
3541:Nuclear Physics B
3497:Physics Letters B
3310:Nuclear Physics B
3259:Physics Letters B
3029:Annals of Physics
2921:Nuclear Physics B
2734:Physical Review D
2583:Nuclear Physics B
2544:Nuclear Physics B
2509:Physics Letters B
2438:Nuclear Physics B
2324:Castellani (2016)
2093:
1984:
1956:
1888:coupling constant
1884:= 4 supersymmetry
1745:, is dual to the
1426:{\displaystyle q}
1323:{\displaystyle q}
1303:{\displaystyle e}
1097:
1031:
942:magnetic monopole
814:
813:
545:van Nieuwenhuizen
6063:
6056:Duality theories
5548:String theorists
5488:Lie superalgebra
5440:Twisted K-theory
5398:Spin(7)-manifold
5351:Compactification
5193:Virasoro algebra
4976:Heterotic string
4870:
4863:
4856:
4847:
4846:
4626:11D supergravity
4355:Lie superalgebra
4342:Supermathematics
4281:
4274:
4267:
4258:
4257:
4252:
4222:
4178:
4144:
4131:
4083:
4049:
4025:
3991:
3982:(1–2): 129–146.
3967:
3933:
3905:
3871:
3847:
3813:
3803:
3761:
3736:
3710:
3697:
3663:
3654:(4): 1245–1258.
3639:
3614:(3–4): 321–326.
3602:
3592:
3572:
3528:
3494:
3477:
3451:
3423:
3413:
3389:
3364:(9): 1357–1437.
3341:
3307:
3290:
3249:
3215:
3206:(4–5): 213–326.
3191:
3151:
3111:
3077:
3053:
3052:
3024:
3018:
3017:
2983:
2963:
2957:
2956:
2954:
2936:
2912:
2906:
2905:
2871:
2851:
2845:
2844:
2810:
2790:
2784:
2783:
2749:
2729:
2723:
2722:
2688:
2668:
2662:
2661:
2636:(5): 1741–1743.
2625:
2619:
2618:
2616:
2598:
2574:
2568:
2567:
2539:
2533:
2532:
2515:(4–6): 304–308.
2504:
2498:
2492:
2486:
2480:
2474:
2468:
2462:
2461:
2433:
2427:
2421:
2415:
2409:
2403:
2397:
2388:
2382:
2376:
2370:
2364:
2358:
2352:
2346:
2327:
2318:See for example
2316:
2310:
2300:
2294:
2276:
2270:
2250:
2244:
2241:
2207:
2192:
2177:
2145:
2143:
2142:
2137:
2135:
2134:
2104:
2102:
2101:
2096:
2094:
2092:
2088:
2087:
2077:
2069:
2036:
2034:
2033:
2028:
1998:
1996:
1995:
1990:
1985:
1983:
1982:
1973:
1962:
1957:
1955:
1944:
1847:
1845:
1844:
1839:
1837:
1836:
1820:
1818:
1817:
1812:
1810:
1809:
1793:
1791:
1790:
1785:
1774:
1735:dual to graviton
1719:
1717:
1716:
1711:
1693:
1691:
1690:
1685:
1666:
1664:
1663:
1658:
1621:
1619:
1618:
1613:
1605:
1600:
1599:
1578:
1573:
1572:
1563:
1562:
1545:strongly coupled
1528:
1526:
1525:
1520:
1481:
1466:
1464:
1463:
1458:
1453:
1432:
1430:
1429:
1424:
1409:
1407:
1406:
1401:
1399:
1329:
1327:
1326:
1321:
1309:
1307:
1306:
1301:
1285:
1283:
1282:
1277:
1275:
1263:
1261:
1260:
1255:
1253:
1238:
1236:
1235:
1230:
1228:
1217:
1205:
1203:
1202:
1197:
1195:
1187:
1175:
1173:
1172:
1167:
1165:
1153:
1151:
1150:
1145:
1143:
1128:
1126:
1125:
1120:
1118:
1111:
1099:
1098:
1093:
1088:
1082:
1058:
1033:
1032:
1027:
1022:
1016:
992:
966:famous equations
908:
835:by stating that
806:
799:
792:
208:Related concepts
33:
19:
18:
6071:
6070:
6066:
6065:
6064:
6062:
6061:
6060:
6041:
6040:
6039:
6034:
5543:
5520:
5497:
5444:
5392:
5362:Kähler manifold
5329:
5306:
5299:
5292:
5285:
5278:
5237:
5198:Mirror symmetry
5179:
5165:Brane cosmology
5111:
5060:
5027:
4983:N=2 superstring
4969:Type IIB string
4964:Type IIA string
4939:Polyakov action
4922:
4879:
4874:
4844:
4839:
4733:
4650:
4592:
4536:
4522:Coleman–Mandula
4510:
4471:Seiberg duality
4466:Konishi anomaly
4399:
4336:
4290:
4285:
4255:
4249:
4225:
4142:
4047:hep-lat/0011073
3811:
3708:
3702:Polyakov, A. M.
3492:
3305:
3200:Physics Reports
3160:Physical Review
3156:Dirac, P. A. M.
3116:Dirac, P. A. M.
3075:
3064:Academic papers
3061:
3059:Further reading
3056:
3025:
3021:
2964:
2960:
2913:
2909:
2852:
2848:
2791:
2787:
2730:
2726:
2669:
2665:
2630:Physical Review
2626:
2622:
2575:
2571:
2540:
2536:
2505:
2501:
2493:
2489:
2481:
2477:
2469:
2465:
2434:
2430:
2422:
2418:
2410:
2406:
2400:Polchinski 1996
2398:
2391:
2383:
2379:
2371:
2367:
2359:
2355:
2349:Castellani 2016
2347:
2340:
2336:
2331:
2330:
2317:
2313:
2301:
2297:
2277:
2273:
2257:. According to
2251:
2247:
2242:
2238:
2233:
2208:
2202:
2193:
2189:Susskind (2011)
2187:
2178:
2172:
2152:
2130:
2126:
2124:
2121:
2120:
2083:
2079:
2078:
2070:
2068:
2060:
2057:
2056:
2010:
2007:
2006:
1978:
1974:
1963:
1961:
1948:
1943:
1935:
1932:
1931:
1903:Seiberg duality
1873:
1865:massive gravity
1832:
1828:
1826:
1823:
1822:
1805:
1801:
1799:
1796:
1795:
1767:
1765:
1762:
1761:
1731:Curtright field
1727:
1699:
1696:
1695:
1673:
1670:
1669:
1646:
1643:
1642:
1601:
1595:
1591:
1574:
1568:
1564:
1558:
1554:
1552:
1549:
1548:
1502:
1499:
1498:
1487:Gerard 't Hooft
1482:
1476:
1449:
1438:
1435:
1434:
1418:
1415:
1414:
1397:
1396:
1367:
1340:
1338:
1335:
1334:
1315:
1312:
1311:
1295:
1292:
1291:
1271:
1269:
1266:
1265:
1249:
1247:
1244:
1243:
1224:
1213:
1211:
1208:
1207:
1191:
1183:
1181:
1178:
1177:
1161:
1159:
1156:
1155:
1139:
1137:
1134:
1133:
1116:
1115:
1107:
1100:
1089:
1087:
1086:
1078:
1070:
1059:
1054:
1045:
1044:
1034:
1023:
1021:
1020:
1012:
1004:
993:
988:
978:
976:
973:
972:
958:Michael Faraday
950:
918:string theories
909:
903:
810:
765:
764:
275:
267:
266:
224:Quantum gravity
209:
183:Mirror symmetry
17:
12:
11:
5:
6069:
6059:
6058:
6053:
6051:Gauge theories
6036:
6035:
6033:
6032:
6027:
6022:
6017:
6012:
6007:
6002:
5997:
5992:
5987:
5982:
5977:
5972:
5967:
5962:
5957:
5952:
5947:
5942:
5937:
5932:
5927:
5922:
5917:
5912:
5907:
5902:
5897:
5892:
5887:
5882:
5877:
5872:
5870:Randjbar-Daemi
5867:
5862:
5857:
5852:
5847:
5842:
5837:
5832:
5827:
5822:
5817:
5812:
5807:
5802:
5797:
5792:
5787:
5782:
5777:
5772:
5767:
5762:
5757:
5752:
5747:
5742:
5737:
5732:
5727:
5722:
5717:
5712:
5707:
5702:
5697:
5692:
5687:
5682:
5677:
5672:
5667:
5662:
5657:
5652:
5647:
5642:
5637:
5632:
5627:
5622:
5617:
5612:
5607:
5602:
5597:
5592:
5587:
5582:
5577:
5572:
5567:
5562:
5557:
5551:
5549:
5545:
5544:
5542:
5541:
5536:
5530:
5528:
5522:
5521:
5519:
5518:
5513:
5507:
5505:
5499:
5498:
5496:
5495:
5493:Lie supergroup
5490:
5485:
5480:
5475:
5470:
5465:
5460:
5454:
5452:
5446:
5445:
5443:
5442:
5437:
5432:
5427:
5422:
5417:
5412:
5407:
5402:
5401:
5400:
5395:
5390:
5386:
5385:
5384:
5374:
5364:
5359:
5353:
5348:
5343:
5337:
5335:
5331:
5330:
5328:
5327:
5319:
5314:
5309:
5304:
5297:
5290:
5283:
5276:
5268:
5263:
5258:
5253:
5247:
5245:
5239:
5238:
5236:
5235:
5230:
5225:
5220:
5215:
5210:
5205:
5200:
5195:
5189:
5187:
5181:
5180:
5178:
5177:
5172:
5170:Quiver diagram
5167:
5162:
5157:
5152:
5147:
5142:
5137:
5132:
5127:
5121:
5119:
5113:
5112:
5110:
5109:
5104:
5099:
5094:
5089:
5084:
5079:
5074:
5068:
5066:
5062:
5061:
5059:
5058:
5053:
5048:
5043:
5037:
5035:
5033:String duality
5029:
5028:
5026:
5025:
5020:
5015:
5010:
5005:
5000:
4995:
4990:
4985:
4980:
4979:
4978:
4973:
4972:
4971:
4966:
4959:Type II string
4956:
4946:
4941:
4936:
4930:
4928:
4924:
4923:
4921:
4920:
4915:
4914:
4913:
4908:
4898:
4896:Cosmic strings
4893:
4887:
4885:
4881:
4880:
4873:
4872:
4865:
4858:
4850:
4841:
4840:
4838:
4837:
4832:
4827:
4822:
4817:
4812:
4807:
4802:
4797:
4792:
4787:
4782:
4777:
4772:
4767:
4762:
4757:
4752:
4747:
4741:
4739:
4735:
4734:
4732:
4731:
4726:
4721:
4716:
4711:
4706:
4701:
4696:
4691:
4686:
4681:
4676:
4671:
4666:
4660:
4658:
4652:
4651:
4649:
4648:
4643:
4638:
4633:
4628:
4623:
4618:
4613:
4608:
4602:
4600:
4594:
4593:
4591:
4590:
4585:
4580:
4575:
4570:
4565:
4560:
4555:
4550:
4544:
4542:
4541:Field theories
4538:
4537:
4535:
4534:
4529:
4524:
4518:
4516:
4512:
4511:
4509:
4508:
4503:
4498:
4493:
4488:
4483:
4478:
4473:
4468:
4463:
4458:
4453:
4448:
4443:
4438:
4436:Superpotential
4433:
4428:
4423:
4421:Supermultiplet
4418:
4413:
4407:
4405:
4401:
4400:
4398:
4397:
4392:
4387:
4382:
4377:
4372:
4367:
4362:
4357:
4352:
4346:
4344:
4338:
4337:
4335:
4334:
4329:
4324:
4319:
4314:
4309:
4304:
4298:
4296:
4295:General topics
4292:
4291:
4284:
4283:
4276:
4269:
4261:
4254:
4253:
4247:
4231:
4224:
4223:
4179:
4153:(2): 276–284.
4132:
4098:(1): 174–181.
4084:
4040:(1–3): 35–48.
4026:
3989:hep-th/9411149
3968:
3931:hep-th/9407087
3906:
3869:hep-th/9607201
3852:Schwarz, J. H.
3848:
3804:
3737:
3719:(6): 194–195.
3698:
3661:hep-th/9607050
3644:Polchinski, J.
3640:
3603:
3590:hep-th/0104063
3573:
3533:Nielsen, H. B.
3529:
3503:(1): 117–120.
3478:
3449:hep-th/0604151
3424:
3411:hep-th/9603086
3390:
3342:
3291:
3250:
3213:hep-th/9412184
3192:
3166:(7): 817–830.
3152:
3126:(821): 60–72.
3112:
3067:
3060:
3057:
3055:
3054:
3035:(2): 167–208.
3019:
2958:
2907:
2846:
2785:
2747:hep-th/0210278
2724:
2686:hep-th/0107149
2663:
2620:
2569:
2534:
2499:
2487:
2475:
2463:
2428:
2416:
2404:
2389:
2377:
2365:
2353:
2337:
2335:
2332:
2329:
2328:
2320:Rickles (2015)
2311:
2295:
2291:Juan Maldacena
2271:
2267:Schwarz (1997)
2259:Jeffery Harvey
2245:
2235:
2234:
2232:
2229:
2200:
2185:
2170:
2151:
2148:
2133:
2129:
2106:
2105:
2091:
2086:
2082:
2076:
2073:
2067:
2064:
2038:
2037:
2026:
2023:
2020:
2017:
2014:
2000:
1999:
1988:
1981:
1977:
1972:
1969:
1966:
1960:
1954:
1951:
1947:
1942:
1939:
1872:
1869:
1848:supergravity.
1835:
1831:
1808:
1804:
1783:
1780:
1777:
1773:
1770:
1726:
1723:
1709:
1706:
1703:
1683:
1680:
1677:
1656:
1653:
1650:
1626:Claus Montonen
1611:
1608:
1604:
1598:
1594:
1590:
1587:
1584:
1581:
1577:
1571:
1567:
1561:
1557:
1518:
1515:
1512:
1509:
1506:
1474:
1456:
1452:
1448:
1445:
1442:
1422:
1411:
1410:
1395:
1392:
1389:
1386:
1383:
1380:
1377:
1374:
1371:
1368:
1364:
1361:
1358:
1355:
1352:
1349:
1346:
1343:
1342:
1319:
1299:
1274:
1252:
1227:
1223:
1220:
1216:
1194:
1190:
1186:
1164:
1142:
1130:
1129:
1114:
1110:
1106:
1103:
1101:
1096:
1092:
1085:
1081:
1077:
1074:
1071:
1068:
1065:
1062:
1060:
1057:
1053:
1050:
1047:
1046:
1043:
1040:
1037:
1035:
1030:
1026:
1019:
1015:
1011:
1008:
1005:
1002:
999:
996:
994:
991:
987:
984:
981:
980:
949:
946:
901:
879:Claus Montonen
844:quasiparticles
812:
811:
809:
808:
801:
794:
786:
783:
782:
781:
780:
775:
767:
766:
763:
762:
757:
752:
747:
742:
737:
732:
727:
722:
717:
712:
707:
702:
697:
692:
687:
682:
677:
672:
667:
662:
657:
652:
647:
642:
637:
632:
627:
622:
617:
612:
607:
602:
597:
595:Randjbar-Daemi
592:
587:
582:
577:
572:
567:
562:
557:
552:
547:
542:
537:
532:
527:
522:
517:
512:
507:
502:
497:
492:
487:
482:
477:
472:
467:
462:
457:
452:
447:
442:
437:
432:
427:
422:
417:
412:
407:
402:
397:
392:
387:
382:
377:
372:
367:
362:
357:
352:
347:
342:
337:
332:
327:
322:
317:
312:
307:
302:
297:
292:
287:
282:
276:
273:
272:
269:
268:
265:
264:
259:
254:
249:
241:
236:
231:
226:
221:
216:
210:
207:
206:
203:
202:
201:
200:
195:
193:Vertex algebra
190:
185:
180:
172:
171:
167:
166:
165:
164:
159:
154:
146:
145:
141:
140:
139:
138:
133:
128:
123:
118:
113:
105:
104:
100:
99:
98:
97:
79:
71:
70:
66:
65:
64:
63:
58:
53:
48:
40:
39:
35:
34:
26:
25:
15:
9:
6:
4:
3:
2:
6068:
6057:
6054:
6052:
6049:
6048:
6046:
6031:
6028:
6026:
6023:
6021:
6018:
6016:
6015:Zamolodchikov
6013:
6011:
6010:Zamolodchikov
6008:
6006:
6003:
6001:
5998:
5996:
5993:
5991:
5988:
5986:
5983:
5981:
5978:
5976:
5973:
5971:
5968:
5966:
5963:
5961:
5958:
5956:
5953:
5951:
5948:
5946:
5943:
5941:
5938:
5936:
5933:
5931:
5928:
5926:
5923:
5921:
5918:
5916:
5913:
5911:
5908:
5906:
5903:
5901:
5898:
5896:
5893:
5891:
5888:
5886:
5883:
5881:
5878:
5876:
5873:
5871:
5868:
5866:
5863:
5861:
5858:
5856:
5853:
5851:
5848:
5846:
5843:
5841:
5838:
5836:
5833:
5831:
5828:
5826:
5823:
5821:
5818:
5816:
5813:
5811:
5808:
5806:
5803:
5801:
5798:
5796:
5793:
5791:
5788:
5786:
5783:
5781:
5778:
5776:
5773:
5771:
5768:
5766:
5763:
5761:
5758:
5756:
5753:
5751:
5748:
5746:
5743:
5741:
5738:
5736:
5733:
5731:
5728:
5726:
5723:
5721:
5718:
5716:
5713:
5711:
5708:
5706:
5703:
5701:
5698:
5696:
5693:
5691:
5688:
5686:
5683:
5681:
5678:
5676:
5673:
5671:
5668:
5666:
5663:
5661:
5658:
5656:
5653:
5651:
5648:
5646:
5643:
5641:
5638:
5636:
5633:
5631:
5628:
5626:
5623:
5621:
5618:
5616:
5613:
5611:
5608:
5606:
5603:
5601:
5598:
5596:
5593:
5591:
5588:
5586:
5583:
5581:
5578:
5576:
5573:
5571:
5568:
5566:
5563:
5561:
5558:
5556:
5553:
5552:
5550:
5546:
5540:
5537:
5535:
5534:Matrix theory
5532:
5531:
5529:
5527:
5523:
5517:
5514:
5512:
5509:
5508:
5506:
5504:
5500:
5494:
5491:
5489:
5486:
5484:
5481:
5479:
5476:
5474:
5471:
5469:
5466:
5464:
5461:
5459:
5456:
5455:
5453:
5451:
5450:Supersymmetry
5447:
5441:
5438:
5436:
5433:
5431:
5428:
5426:
5423:
5421:
5418:
5416:
5413:
5411:
5408:
5406:
5403:
5399:
5396:
5394:
5387:
5383:
5380:
5379:
5378:
5375:
5373:
5370:
5369:
5368:
5365:
5363:
5360:
5357:
5354:
5352:
5349:
5347:
5344:
5342:
5339:
5338:
5336:
5332:
5326:
5324:
5320:
5318:
5315:
5313:
5310:
5307:
5300:
5293:
5286:
5279:
5272:
5269:
5267:
5264:
5262:
5259:
5257:
5254:
5252:
5249:
5248:
5246:
5244:
5240:
5234:
5231:
5229:
5226:
5224:
5221:
5219:
5216:
5214:
5211:
5209:
5206:
5204:
5201:
5199:
5196:
5194:
5191:
5190:
5188:
5186:
5182:
5176:
5173:
5171:
5168:
5166:
5163:
5161:
5158:
5156:
5153:
5151:
5148:
5146:
5143:
5141:
5138:
5136:
5133:
5131:
5128:
5126:
5123:
5122:
5120:
5118:
5114:
5108:
5105:
5103:
5102:Dual graviton
5100:
5098:
5095:
5093:
5090:
5088:
5085:
5083:
5080:
5078:
5075:
5073:
5070:
5069:
5067:
5063:
5057:
5054:
5052:
5049:
5047:
5044:
5042:
5039:
5038:
5036:
5034:
5030:
5024:
5021:
5019:
5018:RNS formalism
5016:
5014:
5011:
5009:
5006:
5004:
5001:
4999:
4996:
4994:
4991:
4989:
4986:
4984:
4981:
4977:
4974:
4970:
4967:
4965:
4962:
4961:
4960:
4957:
4955:
4954:Type I string
4952:
4951:
4950:
4947:
4945:
4942:
4940:
4937:
4935:
4932:
4931:
4929:
4925:
4919:
4916:
4912:
4909:
4907:
4904:
4903:
4902:
4899:
4897:
4894:
4892:
4889:
4888:
4886:
4882:
4878:
4877:String theory
4871:
4866:
4864:
4859:
4857:
4852:
4851:
4848:
4836:
4833:
4831:
4828:
4826:
4823:
4821:
4818:
4816:
4813:
4811:
4808:
4806:
4803:
4801:
4798:
4796:
4793:
4791:
4788:
4786:
4783:
4781:
4778:
4776:
4773:
4771:
4768:
4766:
4763:
4761:
4758:
4756:
4753:
4751:
4748:
4746:
4743:
4742:
4740:
4736:
4730:
4727:
4725:
4722:
4720:
4717:
4715:
4712:
4710:
4707:
4705:
4702:
4700:
4697:
4695:
4692:
4690:
4687:
4685:
4682:
4680:
4677:
4675:
4672:
4670:
4667:
4665:
4662:
4661:
4659:
4657:
4656:Superpartners
4653:
4647:
4644:
4642:
4639:
4637:
4634:
4632:
4629:
4627:
4624:
4622:
4619:
4617:
4614:
4612:
4609:
4607:
4604:
4603:
4601:
4599:
4595:
4589:
4586:
4584:
4581:
4579:
4576:
4574:
4571:
4569:
4566:
4564:
4561:
4559:
4556:
4554:
4551:
4549:
4546:
4545:
4543:
4539:
4533:
4530:
4528:
4525:
4523:
4520:
4519:
4517:
4513:
4507:
4504:
4502:
4499:
4497:
4494:
4492:
4489:
4487:
4484:
4482:
4479:
4477:
4474:
4472:
4469:
4467:
4464:
4462:
4459:
4457:
4454:
4452:
4449:
4447:
4444:
4442:
4439:
4437:
4434:
4432:
4429:
4427:
4424:
4422:
4419:
4417:
4414:
4412:
4409:
4408:
4406:
4402:
4396:
4395:Supermanifold
4393:
4391:
4388:
4386:
4383:
4381:
4378:
4376:
4373:
4371:
4368:
4366:
4363:
4361:
4358:
4356:
4353:
4351:
4348:
4347:
4345:
4343:
4339:
4333:
4332:Supergeometry
4330:
4328:
4325:
4323:
4320:
4318:
4315:
4313:
4310:
4308:
4305:
4303:
4302:Supersymmetry
4300:
4299:
4297:
4293:
4289:
4288:Supersymmetry
4282:
4277:
4275:
4270:
4268:
4263:
4262:
4259:
4250:
4244:
4240:
4239:
4233:
4232:
4230:
4229:
4220:
4216:
4212:
4208:
4204:
4200:
4197:(1): 97–101.
4196:
4192:
4188:
4184:
4180:
4176:
4172:
4168:
4164:
4160:
4156:
4152:
4148:
4141:
4137:
4133:
4129:
4125:
4121:
4117:
4113:
4109:
4105:
4101:
4097:
4093:
4089:
4085:
4081:
4077:
4073:
4069:
4065:
4061:
4057:
4053:
4048:
4043:
4039:
4035:
4031:
4027:
4023:
4019:
4015:
4011:
4007:
4003:
3999:
3995:
3990:
3985:
3981:
3977:
3973:
3969:
3965:
3961:
3957:
3953:
3949:
3945:
3941:
3937:
3932:
3927:
3923:
3919:
3915:
3911:
3907:
3903:
3899:
3895:
3891:
3887:
3883:
3879:
3875:
3870:
3865:
3861:
3857:
3853:
3849:
3845:
3841:
3837:
3833:
3829:
3825:
3821:
3817:
3810:
3805:
3801:
3797:
3793:
3789:
3785:
3781:
3777:
3773:
3769:
3765:
3760:
3755:
3751:
3747:
3743:
3738:
3734:
3730:
3726:
3722:
3718:
3714:
3707:
3703:
3699:
3695:
3691:
3687:
3683:
3679:
3675:
3671:
3667:
3662:
3657:
3653:
3649:
3645:
3641:
3637:
3633:
3629:
3625:
3621:
3617:
3613:
3609:
3604:
3600:
3596:
3591:
3586:
3582:
3578:
3574:
3570:
3566:
3562:
3558:
3554:
3550:
3546:
3542:
3538:
3534:
3530:
3526:
3522:
3518:
3514:
3510:
3506:
3502:
3498:
3491:
3487:
3483:
3479:
3475:
3471:
3467:
3463:
3459:
3455:
3450:
3445:
3441:
3437:
3433:
3429:
3425:
3421:
3417:
3412:
3407:
3403:
3399:
3395:
3394:Harvey, J. A.
3391:
3387:
3383:
3379:
3375:
3371:
3367:
3363:
3359:
3355:
3351:
3347:
3343:
3339:
3335:
3331:
3327:
3323:
3319:
3315:
3311:
3304:
3300:
3297:; Nuyts, J.;
3296:
3292:
3288:
3284:
3280:
3276:
3272:
3268:
3264:
3260:
3256:
3251:
3247:
3243:
3239:
3235:
3231:
3227:
3223:
3219:
3214:
3209:
3205:
3201:
3197:
3193:
3189:
3185:
3181:
3177:
3173:
3169:
3165:
3161:
3157:
3153:
3149:
3145:
3141:
3137:
3133:
3129:
3125:
3121:
3117:
3113:
3109:
3105:
3101:
3097:
3093:
3089:
3085:
3081:
3074:
3069:
3068:
3066:
3065:
3050:
3046:
3042:
3038:
3034:
3030:
3023:
3015:
3011:
3007:
3003:
2999:
2995:
2991:
2987:
2982:
2977:
2973:
2969:
2962:
2953:
2948:
2944:
2940:
2935:
2930:
2926:
2922:
2918:
2911:
2903:
2899:
2895:
2891:
2887:
2883:
2879:
2875:
2870:
2865:
2861:
2857:
2850:
2842:
2838:
2834:
2830:
2826:
2822:
2818:
2814:
2809:
2804:
2800:
2796:
2789:
2781:
2777:
2773:
2769:
2765:
2761:
2757:
2753:
2748:
2743:
2740:(4): 044010.
2739:
2735:
2728:
2720:
2716:
2712:
2708:
2704:
2700:
2696:
2692:
2687:
2682:
2678:
2674:
2667:
2659:
2655:
2651:
2647:
2643:
2639:
2635:
2631:
2624:
2615:
2610:
2606:
2602:
2597:
2592:
2588:
2584:
2580:
2573:
2565:
2561:
2557:
2553:
2549:
2545:
2538:
2530:
2526:
2522:
2518:
2514:
2510:
2503:
2496:
2491:
2484:
2479:
2472:
2467:
2459:
2455:
2451:
2447:
2443:
2439:
2432:
2425:
2424:Polyakov 1974
2420:
2413:
2412:'t Hooft 1974
2408:
2402:, p. 12.
2401:
2396:
2394:
2386:
2381:
2375:, p. 30.
2374:
2369:
2362:
2357:
2350:
2345:
2343:
2338:
2325:
2321:
2315:
2308:
2304:
2299:
2292:
2288:
2286:
2281:
2275:
2269:, p. 3.
2268:
2264:
2260:
2256:
2249:
2240:
2236:
2228:
2226:
2222:
2218:
2214:
2205:
2199:
2191:, p. 178
2190:
2184:
2175:
2169:
2164:
2162:
2157:
2147:
2131:
2127:
2118:
2115:
2111:
2089:
2084:
2080:
2074:
2071:
2062:
2055:
2054:
2053:
2051:
2047:
2043:
2024:
2021:
2018:
2012:
2005:
2004:
2003:
1986:
1979:
1975:
1970:
1967:
1964:
1958:
1952:
1949:
1945:
1940:
1937:
1930:
1929:
1928:
1925:
1923:
1919:
1915:
1913:
1906:
1904:
1900:
1896:
1892:
1889:
1885:
1883:
1878:
1868:
1866:
1862:
1858:
1854:
1849:
1833:
1829:
1806:
1802:
1778:
1759:
1754:
1752:
1748:
1744:
1740:
1736:
1732:
1722:
1707:
1704:
1701:
1681:
1678:
1675:
1654:
1651:
1648:
1640:
1636:
1631:
1627:
1622:
1609:
1606:
1602:
1596:
1592:
1588:
1582:
1579:
1575:
1569:
1565:
1559:
1555:
1546:
1542:
1541:weak coupling
1537:
1535:
1531:
1513:
1507:
1504:
1496:
1492:
1488:
1480:, p. 817
1479:
1473:
1468:
1454:
1450:
1443:
1440:
1420:
1393:
1390:
1387:
1384:
1381:
1378:
1375:
1372:
1369:
1362:
1356:
1353:
1350:
1347:
1344:
1333:
1332:
1331:
1317:
1297:
1289:
1240:
1221:
1112:
1104:
1102:
1094:
1083:
1075:
1066:
1063:
1061:
1051:
1041:
1038:
1036:
1028:
1017:
1009:
1000:
997:
995:
985:
971:
970:
969:
967:
963:
959:
955:
945:
943:
939:
935:
931:
927:
923:
919:
915:
907:, p. 117
906:
900:
896:
894:
893:
888:
884:
880:
876:
872:
870:
865:
861:
857:
853:
849:
845:
842:
838:
834:
830:
826:
822:
818:
807:
802:
800:
795:
793:
788:
787:
785:
784:
779:
776:
774:
771:
770:
769:
768:
761:
758:
756:
753:
751:
748:
746:
745:Zamolodchikov
743:
741:
740:Zamolodchikov
738:
736:
733:
731:
728:
726:
723:
721:
718:
716:
713:
711:
708:
706:
703:
701:
698:
696:
693:
691:
688:
686:
683:
681:
678:
676:
673:
671:
668:
666:
663:
661:
658:
656:
653:
651:
648:
646:
643:
641:
638:
636:
633:
631:
628:
626:
623:
621:
618:
616:
613:
611:
608:
606:
603:
601:
598:
596:
593:
591:
588:
586:
583:
581:
578:
576:
573:
571:
568:
566:
563:
561:
558:
556:
553:
551:
548:
546:
543:
541:
538:
536:
533:
531:
528:
526:
523:
521:
518:
516:
513:
511:
508:
506:
503:
501:
498:
496:
493:
491:
488:
486:
483:
481:
478:
476:
473:
471:
468:
466:
463:
461:
458:
456:
453:
451:
448:
446:
443:
441:
438:
436:
433:
431:
428:
426:
423:
421:
418:
416:
413:
411:
408:
406:
403:
401:
398:
396:
393:
391:
388:
386:
383:
381:
378:
376:
373:
371:
368:
366:
363:
361:
358:
356:
353:
351:
348:
346:
343:
341:
338:
336:
333:
331:
328:
326:
323:
321:
318:
316:
313:
311:
308:
306:
303:
301:
298:
296:
293:
291:
288:
286:
283:
281:
278:
277:
271:
270:
263:
260:
258:
255:
253:
250:
248:
246:
242:
240:
237:
235:
232:
230:
229:Supersymmetry
227:
225:
222:
220:
217:
215:
212:
211:
205:
204:
199:
196:
194:
191:
189:
186:
184:
181:
179:
176:
175:
174:
173:
169:
168:
163:
160:
158:
155:
153:
152:Phenomenology
150:
149:
148:
147:
144:Phenomenology
143:
142:
137:
134:
132:
129:
127:
124:
122:
119:
117:
114:
112:
109:
108:
107:
106:
102:
101:
95:
91:
87:
83:
80:
78:
75:
74:
73:
72:
68:
67:
62:
59:
57:
54:
52:
51:Cosmic string
49:
47:
44:
43:
42:
41:
37:
36:
32:
28:
27:
24:
23:String theory
21:
20:
5560:Arkani-Hamed
5458:Supergravity
5425:Moduli space
5322:
5317:Dirac string
5243:Gauge theory
5223:Loop algebra
5160:Black string
5055:
5023:GS formalism
4598:Supergravity
4505:
4491:Localization
4481:Witten index
4456:Moduli space
4350:Superalgebra
4317:Supergravity
4237:
4227:
4226:
4194:
4190:
4187:Olive, D. I.
4150:
4146:
4136:'t Hooft, G.
4095:
4091:
4088:Susskind, L.
4037:
4033:
3979:
3975:
3924:(1): 19–52.
3921:
3917:
3859:
3855:
3819:
3815:
3749:
3745:
3742:Moessner, R.
3716:
3713:JETP Letters
3712:
3651:
3647:
3611:
3607:
3580:
3577:Olive, D. I.
3544:
3540:
3500:
3496:
3486:Olive, D. I.
3482:Montonen, C.
3439:
3435:
3428:Kapustin, A.
3401:
3397:
3361:
3357:
3350:Olive, D. I.
3313:
3309:
3299:Olive, D. I.
3265:(1): 35–43.
3262:
3258:
3203:
3199:
3163:
3159:
3123:
3119:
3083:
3079:
3063:
3062:
3032:
3028:
3022:
2971:
2967:
2961:
2924:
2920:
2910:
2859:
2855:
2849:
2798:
2794:
2788:
2737:
2733:
2727:
2676:
2672:
2666:
2633:
2629:
2623:
2586:
2582:
2572:
2547:
2543:
2537:
2512:
2508:
2502:
2490:
2478:
2466:
2441:
2437:
2431:
2419:
2407:
2380:
2368:
2363:, p. 3.
2361:Schwarz 1997
2356:
2351:, p. 1.
2314:
2307:Dirac (1948)
2303:Dirac (1931)
2298:
2284:
2274:
2262:
2248:
2239:
2210:
2204:Olive (2001)
2196:
2181:
2166:
2156:reductionism
2153:
2116:
2109:
2107:
2045:
2041:
2039:
2001:
1926:
1917:
1911:
1907:
1894:
1890:
1881:
1879:theory with
1874:
1860:
1856:
1852:
1850:
1755:
1728:
1725:Dual gravity
1623:
1538:
1484:
1478:Dirac (1948)
1470:
1412:
1241:
1131:
951:
911:
898:
890:
868:
820:
816:
815:
285:Arkani-Hamed
244:
234:Supergravity
5920:Silverstein
5420:Orientifold
5155:Black holes
5150:Black brane
5107:Dual photon
4738:Researchers
4724:Stop squark
4689:Graviscalar
4684:Graviphoton
4548:Wess–Zumino
4411:Supercharge
3972:Seiberg, N.
3910:Seiberg, N.
3862:(2): 1–32.
3316:(1): 1–28.
3295:Goddard, P.
3196:Duff, M. J.
3086:: 100–108.
2550:: 413–424.
2495:Osborn 1979
2373:Harvey 1996
2206:, p. 5
2176:, p. 3
2161:emergentism
1922:theta-angle
1920:as well as
1901:. See also
1630:David Olive
887:David Olive
645:Silverstein
170:Mathematics
82:Superstring
6045:Categories
5940:Strominger
5935:Steinhardt
5930:Staudacher
5845:Polchinski
5795:Nanopoulos
5755:Mandelstam
5735:Kontsevich
5575:Berenstein
5503:Holography
5483:Superspace
5382:K3 surface
5341:Worldsheet
5256:Instantons
4884:Background
4785:Iliopoulos
4729:Superghost
4719:Sgoldstino
4704:Neutralino
4496:Mu problem
4416:R-symmetry
4380:Superspace
4375:Supergroup
4183:Witten, E.
3914:Witten, E.
3759:1605.05874
3740:Rehn, J.;
3432:Witten, E.
3346:Goddard, P
2981:1907.11537
2934:1907.11532
2927:: 114777.
2679:(9): 027.
2596:1907.11530
2589:: 114784.
2385:Dirac 1931
2334:References
2174:Sen (2001)
1877:Yang–Mills
1288:Paul Dirac
1286:? In 1931
885:physicist
877:physicist
665:Strominger
660:Steinhardt
655:Staudacher
570:Polchinski
520:Nanopoulos
480:Mandelstam
460:Kontsevich
300:Berenstein
257:Multiverse
5975:Veneziano
5855:Rajaraman
5750:Maldacena
5640:Gopakumar
5590:Dijkgraaf
5585:Curtright
5251:Anomalies
5130:NS5-brane
5051:U-duality
5046:S-duality
5041:T-duality
4755:Batchelor
4679:Goldstino
4568:Super QCD
4446:FI D-term
4431:BPS state
4219:0370-2693
4175:1874/4686
4128:189843984
4120:0015-9018
4072:0920-5632
4014:0550-3213
3956:0550-3213
3894:0920-5632
3844:1355-2198
3822:: 62–67.
3800:206159482
3784:1364-503X
3733:0370-274X
3686:0034-6861
3636:0370-2693
3569:0550-3213
3547:: 45–61.
3525:0370-2693
3442:: 1–236.
3386:0034-4885
3338:0550-3213
3287:0370-2693
3246:119524337
3238:0370-1573
3188:0031-899X
3148:1364-5021
3108:1355-2198
3014:198953238
3006:1029-8479
2974:(9): 63.
2894:1029-8479
2869:1307.8295
2862:(2): 75.
2841:119240022
2833:1029-8479
2808:1111.1642
2801:(2): 18.
2772:0556-2821
2711:1029-8479
2658:0031-899X
2444:: 45–61.
2090:τ
2072:−
2066:↦
2063:τ
2019:τ
2016:↦
2013:τ
1968:π
1953:π
1946:θ
1938:τ
1739:Curtright
1635:Ed Witten
1610:α
1586:ℏ
1583:π
1556:α
1508:
1447:ℏ
1444:π
1391:±
1382:±
1360:ℏ
1357:π
1222:−
1219:→
1189:→
1095:˙
1084:−
1076:×
1073:∇
1052:⋅
1049:∇
1029:˙
1010:×
1007:∇
1001:ρ
986:⋅
983:∇
860:electrons
829:S-duality
705:Veneziano
580:Rajaraman
475:Maldacena
365:Gopakumar
315:Dijkgraaf
310:Curtright
274:Theorists
162:Landscape
157:Cosmology
121:U-duality
116:T-duality
111:S-duality
94:Heterotic
6030:Zwiebach
5985:Verlinde
5980:Verlinde
5955:Townsend
5950:Susskind
5885:Sagnotti
5850:Polyakov
5805:Nekrasov
5770:Minwalla
5765:Martinec
5730:Knizhnik
5725:Klebanov
5720:Kapustin
5685:'t Hooft
5620:Fischler
5555:Aganagić
5526:M-theory
5415:Conifold
5410:Orbifold
5393:manifold
5334:Geometry
5140:M5-brane
5135:M2-brane
5072:Graviton
4988:F-theory
4790:Montonen
4714:Sfermion
4709:R-hadron
4694:Higgsino
4669:Chargino
4558:4D N = 1
4515:Theorems
4404:Concepts
4138:(1974).
4080:17842520
4022:18466754
3964:14361074
3792:27458263
3704:(1974).
3694:14147542
3488:(1977).
3474:30505126
3352:(1978).
3301:(1977).
2902:53538737
2780:14739195
2201:—
2186:—
2183:gravity.
2171:—
1855:= 4 and
1624:In 1977
1495:solitons
1475:—
902:—
848:solitons
841:emergent
778:Glossary
760:Zwiebach
715:Verlinde
710:Verlinde
685:Townsend
680:'t Hooft
675:Susskind
610:Sagnotti
575:Polyakov
530:Nekrasov
495:Minwalla
490:Martinec
455:Knizhnik
450:Klebanov
445:Kapustin
415:Horowitz
345:Fischler
280:Aganagić
198:K-theory
131:F-theory
126:M-theory
5960:Trivedi
5945:Sundrum
5910:Shenker
5900:Seiberg
5895:Schwarz
5865:Randall
5825:Novikov
5815:Nielsen
5800:Năstase
5710:Kallosh
5695:Gibbons
5635:Gliozzi
5625:Friedan
5615:Ferrara
5600:Douglas
5595:Distler
5145:S-brane
5125:D-brane
5082:Tachyon
5077:Dilaton
4891:Strings
4805:Seiberg
4780:Golfand
4760:Berezin
4745:Affleck
4674:Gaugino
4199:Bibcode
4155:Bibcode
4100:Bibcode
4052:Bibcode
4030:Sen, A.
3994:Bibcode
3936:Bibcode
3902:7541625
3874:Bibcode
3824:Bibcode
3764:Bibcode
3721:Bibcode
3666:Bibcode
3616:Bibcode
3595:Bibcode
3549:Bibcode
3505:Bibcode
3454:Bibcode
3416:Bibcode
3366:Bibcode
3318:Bibcode
3267:Bibcode
3218:Bibcode
3168:Bibcode
3128:Bibcode
3088:Bibcode
3037:Bibcode
2986:Bibcode
2939:Bibcode
2874:Bibcode
2813:Bibcode
2752:Bibcode
2719:9901270
2691:Bibcode
2638:Bibcode
2601:Bibcode
2552:Bibcode
2517:Bibcode
2446:Bibcode
2168:system.
2050:abelian
1497:, in a
883:British
875:Finnish
773:History
690:Trivedi
670:Sundrum
635:Shenker
625:Seiberg
620:Schwarz
590:Randall
550:Novikov
540:Nielsen
525:Năstase
435:Kallosh
420:Gibbons
360:Gliozzi
350:Friedan
340:Ferrara
325:Douglas
320:Distler
90:Type II
77:Bosonic
61:D-brane
6025:Zumino
6020:Zaslow
6005:Yoneya
5995:Witten
5915:Siegel
5890:Scherk
5860:Ramond
5835:Ooguri
5760:Marolf
5715:Kaluza
5700:Kachru
5690:Hořava
5680:Harvey
5675:Hanson
5660:Gubser
5650:Greene
5580:Bousso
5565:Atiyah
5117:Branes
4927:Theory
4835:Zumino
4830:Witten
4820:Rogers
4810:Siegel
4750:Bagger
4451:F-term
4441:D-term
4245:
4217:
4126:
4118:
4078:
4070:
4020:
4012:
3962:
3954:
3900:
3892:
3842:
3798:
3790:
3782:
3731:
3692:
3684:
3634:
3567:
3523:
3472:
3404:: 66.
3384:
3336:
3285:
3244:
3236:
3186:
3146:
3106:
3012:
3004:
2900:
2892:
2839:
2831:
2778:
2770:
2717:
2709:
2656:
1747:Freund
1743:Freund
1641:, the
755:Zumino
750:Zaslow
735:Yoneya
725:Witten
640:Siegel
615:Scherk
585:Ramond
560:Ooguri
485:Marolf
440:Kaluza
425:Kachru
410:Hořava
405:Harvey
400:Hanson
385:Gubser
375:Greene
305:Bousso
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